10th Class Mathematics Real Numbers Question Bank Case Based (MCQs) - Real Numbers

In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number of participants that can accommodated in each room are:

A) 14

B) 12

C) 16

D) 18

Correct Answer: B

Solution :

Sol. Using prime factorsation:

\[60=2\times 2\times 3\times 5={{2}^{2}}\times 3\times 5\]

\[84=2\times 2\times 3\times 7={{2}^{2}}\times 3\times 7\]

and \[108=2\times 2\times 3\times 3\times 3={{2}^{2}}\times {{3}^{3}}\]

\[\therefore \] Maximum number of participants that can be accommodated in each room \[=HCF(60,84,108)\]

= Product of the smallest power of each common prime factor in the numbers.

\[={{2}^{2}}\times 3=4\times 3=12\]

So, option [b] is correct.